I worked at Amazon (AWS specifically) and am in Seattle. I learned a lot and am very proud of what my teams accomplished at Amazon.
To the specific question around this thread - there's a lot of discussion online including this discussion of the Amazon "Leadership Principles" (amazon.jobs/principles)
I was an Amazon bar raiser like the post above as well as a Microsoft "As Appropriate" interviewer which is the Microsoft equivalent. Bar raisers are intended to ensure that candidates are a good cultural fit in terms of the leadership principles as well as meeting the job requirements. The leadership principles are very much pivotal to Amazon's success in my opinion.
I would add that different parts of Amazon have subcultures in terms of AWS and Kindle being somewhat different from each other and each certainly different than the old core book business and broader retail business. In my opinion each SVP had a sub-culture some of which is called out in elements of the NYT story. So while this is painted as Amazon overall I don't think that part of the NYT story is accurate as it overly generalizes individual managers and individual anecdotes as the company overall -- painting a harsh picture of Amazon. Some people do really love working at Amazon ad figure out a way to make Amazon a great place to work as long as they elect to be there. There are many options for talented people and elements of Amazon can be quite attractive for instance getting a lot done and having compelling work.
Also managers have a lot of autonomy so who you work with and for matters as with most companies and jobs. There are good managers in most companies. And there are bad managers everywhere who show poor judgment and act inappropriately. I'm not making excuses just calling out a reality that a story or stories could be written about any number of companies where managers take actions that no one would want to read about in the NYT or elsewhere. For instance plenty of articles have been written about the Microsoft stack ranking system, which I won't go into any detail about here. (See:http://www.forbes.com/sites/petercohan/2012/07/13/why-stack-ranking-worked-better-at-ge-than-microsoft )
I would agree with the earlier post here that Amazon is not a country club, is very frugal, has tremendous customer focus and is extremely analytical. Amazon also hires smart, committed leaders who it entrusts to work with autonomy which is also a core element of the company's success and culture. You can also read the rest of the principles above as they guide a lot of the day-to-day at Amazon. You'll note with all the positives there are no Amazon principles around taking care of their own teams. As a comparison I was really surprised to observe how John Chambers of Cisco led and talked about the "Cisco family" which has its own set of positives and negatives and is very different from Amazon on this element of culture. (See: inc.com/john-chambers/treat-employees-like-family.html)
And the attrition while "in line" with the industry according to Jay Carney isn't for everyone and certainly doesn't treat employees as well as Google, Netflix or some other employers (See:businessinsider.com/jay-carney-defends-amazon-this-is-an-incredibly-compelling-place-to-work-2015-8?ncid=newsltushpmg00000003). I wouldn't expect to see Amazon match many of the benefits of other companies. For instance, many engineers on my Amazon teams bought their own extra monitors, SSD hard drives, etc. As a matter of fact, so did I. It was the first and only employer I worked for where I bought computer gear to use everyday at work with my own money and paid for the cell phone I needed to do my job etc. So the discussion of "entitlement" is accurate if you expect an employer to provide all of the tools needed to be effective in your day-to-day role. You certainly don't have to do any of those things but many people do and did that at Amazon. That is different than other tech companies and I'm not clear everything in Amazon's culture is a net positive.
But this story isn't new you can read more in the Brad Stone book - (See: geekwire.com/2014/jeff-bezos-casts-intimidating-presence-prayed-heart-attack-rather-face-wrath )
Personally, I learned a lot, worked with committed, hard working peers who built great services but Amazon isn't the only place to work with top-notch people solving problems for customers in a way that builds real businesses. In many ways, elements of this more than anything else are why I decided to leave Amazon when I did.